Abstract
This work investigates the effects of target nuclear deformations upon the high-energy differential elastic and rotational excitation cross sections for neutron scattering. An optical-model potential of cylindrically symmetrical ellipsoidal shape is used to represent the target nucleus. The deformed potential is first oriented parallel to each of the coordinate axes. The differential cross sections are evaluated and averaged over such orientations. Next, the potential is oriented at an arbitrary angle. The differential cross section is evaluated and averaged over all possible orientation angles. The foregoing averaged cross sections are compared with the cross sections obtained by assuming spherical nuclei for the cases of aluminum and lutetium. Third, differential cross sections with the simultaneous excitations of the target nucleus to higher rotational levels are investigated. Results of calculations are shown for a nucleus having the dimensions of lutetium in initial $I=0$ and $I=7$ spin states. Fourth, the cross section and polarization are investigated by assuming a spin-orbit interaction added to the central deformed potential. It is found that for an arbitrary nuclear orientation the polarization generally has a component parallel to the scattering plane. However, such a component vanishes upon averaging over orientations.
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